# جدول تفكيك الأعداد الصحيحة الغاوسية

في نظرية الأعداد، عدد طبيعي غاوسي هو عدد عقدي جزءه الحقيقي وجزءه التخيلي هما عددان صحيحان.
    $\mathbb {Z} [i]=\{a+bi\mid a,b\in \mathbb {Z} \}$ حيث $i={\sqrt {-1}}$.

## معضلات لم تحلحل بعد

تسأل معضلة الدائرة لغاوس عن عدد النقط في مشبك النقط الموجودات داخل دائرة ما مركزها هو مركز المعلم. يكافئ هذا السؤال ما يلي: كم عدد الأعداد الصحيحة الغاوسية الذين معيارهم لا يتجاوز قيمة معينة ؟

## التفكيك

| المعيار | العدد الصحيح | العامل |
| 2 | 1+i | (p) |
| 4 | 2 | −i·(1+i)$^2$ |
| 5 | 1+2i 2+i | (p) (p) |
| 8 | 2+2i | −i·(1+i)$^3$ |
| 9 | 3 | (p) |
| 10 | 1+3i 3+i | (1+i)·(2+i) (1+i)·(2−i) |
| 13 | 2+3i 3+2i | (p) (p) |
| 16 | 4 | −(1+i)$^4$ |
| 17 | 1+4i 4+i | (p) (p) |
| 18 | 3+3i | (1+i)·3 |
| 20 | 2+4i 4+2i | (1+i)$^2$·(2−i) −i·(1+i)$^2$·(2+i) |
| 25 | 3+4i 4+3i 5 | (2+i)$^2$ i·(2−i)$^2$ (2+i)·(2−i) |
| 26 | 1+5i 5+i | (1+i)·(3+2i) (1+i)·(3−2i) |
| 29 | 2+5i 5+2i | (p) (p) |
| 32 | 4+4i | −(1+i)$^5$ |
| 34 | 3+5i 5+3i | (1+i)·(4+i) (1+i)·(4−i) |
| 36 | 6 | −i·(1+i)$^2$·3 |
| 37 | 1+6i 6+i | (p) (p) |
| 40 | 2+6i 6+2i | −i·(1+i)$^3$·(2+i) −i·(1+i)$^3$·(2−i) |
| 41 | 4+5i 5+4i | (p) (p) |
| 45 | 3+6i 6+3i | i·(2−i)·3 (2+i)·3 |
| 49 | 7 | (p) |
| 50 | 1+7i 5+5i 7+i | i·(1+i)·(2−i)$^2$ (1+i)·(2+i)·(2−i) −i·(1+i)·(2+i)$^2$ |
| 52 | 4+6i 6+4i | (1+i)$^2$·(3−2i) −i·(1+i)$^2$·(3+2i) |
| 53 | 2+7i 7+2i | (p) (p) |
| 58 | 3+7i 7+3i | (1+i)·(5+2i) (1+i)·(5−2i) |
| 61 | 5+6i 6+5i | (p) (p) |
| 64 | 8 | i·(1+i)$^6$ |
| 65 | 1+8i 4+7i 7+4i 8+i | i·(2+i)·(3−2i) (2+i)·(3+2i) i·(2−i)·(3−2i) (2−i)·(3+2i) |
| 68 | 2+8i 8+2i | (1+i)$^2$·(4−i) −i·(1+i)$^2$·(4+i) |
| 72 | 6+6i | −i·(1+i)$^3$·3 |
| 73 | 3+8i 8+3i | (p) (p) |
| 74 | 5+7i 7+5i | (1+i)·(6+i) (1+i)·(6−i) |
| 80 | 4+8i 8+4i | −i·(1+i)$^4$·(2−i) −(1+i)$^4$·(2+i) |
| 81 | 9 | 3$^2$ |
| 82 | 1+9i 9+i | (1+i)·(5+4i) (1+i)·(5−4i) |
| 85 | 2+9i 6+7i 7+6i 9+2i | i·(2−i)·(4+i) i·(2−i)·(4−i) (2+i)·(4+i) (2+i)·(4−i) |
| 89 | 5+8i 8+5i | (p) (p) |
| 90 | 3+9i 9+3i | (1+i)·(2+i)·3 (1+i)·(2−i)·3 |
| 97 | 4+9i 9+4i | (p) (p) |
| 98 | 7+7i | (1+i)·7 |
| 100 | 6+8i 8+6i 10 | −i·(1+i)$^2$·(2+i)$^2$ (1+i)$^2$·(2−i)$^2$ −i·(1+i)$^2$·(2+i)·(2−i) |
| 101 | 1+10i 10+i | (p) (p) |
| 104 | 2+10i 10+2i | −i·(1+i)$^3$·(3+2i) −i·(1+i)$^3$·(3−2i) |
| 106 | 5+9i 9+5i | (1+i)·(7+2i) (1+i)·(7−2i) |
| 109 | 3+10i 10+3i | (p) (p) |
| 113 | 7+8i 8+7i | (p) (p) |
| 116 | 4+10i 10+4i | (1+i)$^2$·(5−2i) −i·(1+i)$^2$·(5+2i) |
| 117 | 6+9i 9+6i | i·3·(3−2i) 3·(3+2i) |
| 121 | 11 | (p) |
| 122 | 1+11i 11+i | (1+i)·(6+5i) (1+i)·(6−5i) |
| 125 | 2+11i 5+10i 10+5i 11+2i | (2+i)$^3$ i·(2+i)·(2−i)$^2$ (2+i)$^2$·(2−i) i·(2−i)$^3$ |
| 128 | 8+8i | i·(1+i)$^7$ |
| 130 | 3+11i 7+9i 9+7i 11+3i | i·(1+i)·(2−i)·(3−2i) (1+i)·(2−i)·(3+2i) (1+i)·(2+i)·(3−2i) −i·(1+i)·(2+i)·(3+2i) |
| 136 | 6+10i 10+6i | −i·(1+i)$^3$·(4+i) −i·(1+i)$^3$·(4−i) |
| 137 | 4+11i 11+4i | (p) (p) |
| 144 | 12 | −(1+i)$^4$·3 |
| 145 | 1+12i 8+9i 9+8i 12+i | i·(2−i)·(5+2i) (2+i)·(5+2i) i·(2−i)·(5−2i) (2+i)·(5−2i) |
| 146 | 5+11i 11+5i | (1+i)·(8+3i) (1+i)·(8−3i) |
| 148 | 2+12i 12+2i | (1+i)$^2$·(6−i) −i·(1+i)$^2$·(6+i) |
| 149 | 7+10i 10+7i | (p) (p) |
| 153 | 3+12i 12+3i | i·3·(4−i) 3·(4+i) |
| 157 | 6+11i 11+6i | (p) (p) |
| 160 | 4+12i 12+4i | −(1+i)$^5$·(2+i) −(1+i)$^5$·(2−i) |
| 162 | 9+9i | (1+i)·3$^2$ |
| 164 | 8+10i 10+8i | (1+i)$^2$·(5−4i) −i·(1+i)$^2$·(5+4i) |
| 169 | 5+12i 12+5i 13 | (3+2i)$^2$ i·(3−2i)$^2$ (3+2i)·(3−2i) |
| 170 | 1+13i 7+11i 11+7i 13+i | (1+i)·(2+i)·(4+i) (1+i)·(2+i)·(4−i) (1+i)·(2−i)·(4+i) (1+i)·(2−i)·(4−i) |
| 173 | 2+13i 13+2i | (p) (p) |
| 178 | 3+13i 13+3i | (1+i)·(8+5i) (1+i)·(8−5i) |
| 180 | 6+12i 12+6i | (1+i)$^2$·(2−i)·3 −i·(1+i)$^2$·(2+i)·3 |
| 181 | 9+10i 10+9i | (p) (p) |
| 185 | 4+13i 8+11i 11+8i 13+4i | i·(2−i)·(6+i) i·(2−i)·(6−i) (2+i)·(6+i) (2+i)·(6−i) |
| 193 | 7+12i 12+7i | (p) (p) |
| 194 | 5+13i 13+5i | (1+i)·(9+4i) (1+i)·(9−4i) |
| 196 | 14 | −i·(1+i)$^2$·7 |
| 197 | 1+14i 14+i | (p) (p) |
| 200 | 2+14i 10+10i 14+2i | (1+i)$^3$·(2−i)$^2$ −i·(1+i)$^3$·(2+i)·(2−i) −(1+i)$^3$·(2+i)$^2$ |
| 202 | 9+11i 11+9i | (1+i)·(10+i) (1+i)·(10−i) |
| 205 | 3+14i 6+13i 13+6i 14+3i | i·(2+i)·(5−4i) (2+i)·(5+4i) i·(2−i)·(5−4i) (2−i)·(5+4i) |
| 208 | 8+12i 12+8i | −i·(1+i)$^4$·(3−2i) −(1+i)$^4$·(3+2i) |
| 212 | 4+14i 14+4i | (1+i)$^2$·(7−2i) −i·(1+i)$^2$·(7+2i) |
| 218 | 7+13i 13+7i | (1+i)·(10+3i) (1+i)·(10−3i) |
| 221 | 5+14i 10+11i 11+10i 14+5i | i·(3−2i)·(4+i) (3+2i)·(4+i) i·(3−2i)·(4−i) (3+2i)·(4−i) |
| 225 | 9+12i 12+9i 15 | (2+i)$^2$·3 i·(2−i)$^2$·3 (2+i)·(2−i)·3 |
| 226 | 1+15i 15+i | (1+i)·(8+7i) (1+i)·(8−7i) |
| 229 | 2+15i 15+2i | (p) (p) |
| 232 | 6+14i 14+6i | −i·(1+i)$^3$·(5+2i) −i·(1+i)$^3$·(5−2i) |
| 233 | 8+13i 13+8i | (p) (p) |
| 234 | 3+15i 15+3i | (1+i)·3·(3+2i) (1+i)·3·(3−2i) |
| 241 | 4+15i 15+4i | (p) (p) |
| 242 | 11+11i | (1+i)·11 |
| 244 | 10+12i 12+10i | (1+i)$^2$·(6−5i) −i·(1+i)$^2$·(6+5i) |
| 245 | 7+14i 14+7i | i·(2−i)·7 (2+i)·7 |
| 250 | 5+15i 9+13i 13+9i 15+5i | (1+i)·(2+i)$^2$·(2−i) i·(1+i)·(2−i)$^3$ −i·(1+i)·(2+i)$^3$ (1+i)·(2+i)·(2−i)$^2$ |
| المعيار | العدد الصحيح | العوامل |
| 256 | 16 | (1+i)$^8$ |
| 257 | 1+16i 16+i | (p) (p) |
| 260 | 2+16i 8+14i 14+8i 16+2i | (1+i)$^2$·(2+i)·(3−2i) −i·(1+i)$^2$·(2+i)·(3+2i) (1+i)$^2$·(2−i)·(3−2i) −i·(1+i)$^2$·(2−i)·(3+2i) |
| 261 | 6+15i 15+6i | i·3·(5−2i) 3·(5+2i) |
| 265 | 3+16i 11+12i 12+11i 16+3i | i·(2−i)·(7+2i) i·(2−i)·(7−2i) (2+i)·(7+2i) (2+i)·(7−2i) |
| 269 | 10+13i 13+10i | (p) (p) |
| 272 | 4+16i 16+4i | −i·(1+i)$^4$·(4−i) −(1+i)$^4$·(4+i) |
| 274 | 7+15i 15+7i | (1+i)·(11+4i) (1+i)·(11−4i) |
| 277 | 9+14i 14+9i | (p) (p) |
| 281 | 5+16i 16+5i | (p) (p) |
| 288 | 12+12i | −(1+i)$^5$·3 |
| 289 | 8+15i 15+8i 17 | i·(4−i)$^2$ (4+i)$^2$ (4+i)·(4−i) |
| 290 | 1+17i 11+13i 13+11i 17+i | i·(1+i)·(2−i)·(5−2i) (1+i)·(2+i)·(5−2i) (1+i)·(2−i)·(5+2i) −i·(1+i)·(2+i)·(5+2i) |
| 292 | 6+16i 16+6i | (1+i)$^2$·(8−3i) −i·(1+i)$^2$·(8+3i) |
| 293 | 2+17i 17+2i | (p) (p) |
| 296 | 10+14i 14+10i | −i·(1+i)$^3$·(6+i) −i·(1+i)$^3$·(6−i) |
| 298 | 3+17i 17+3i | (1+i)·(10+7i) (1+i)·(10−7i) |
| 305 | 4+17i 7+16i 16+7i 17+4i | i·(2+i)·(6−5i) (2+i)·(6+5i) i·(2−i)·(6−5i) (2−i)·(6+5i) |
| 306 | 9+15i 15+9i | (1+i)·3·(4+i) (1+i)·3·(4−i) |
| 313 | 12+13i 13+12i | (p) (p) |
| 314 | 5+17i 17+5i | (1+i)·(11+6i) (1+i)·(11−6i) |
| 317 | 11+14i 14+11i | (p) (p) |
| 320 | 8+16i 16+8i | −(1+i)$^6$·(2−i) i·(1+i)$^6$·(2+i) |
| 324 | 18 | −i·(1+i)$^2$·3$^2$ |
| 325 | 1+18i 6+17i 10+15i 15+10i 17+6i 18+i | (2+i)$^2$·(3+2i) i·(2−i)$^2$·(3+2i) i·(2+i)·(2−i)·(3−2i) (2+i)·(2−i)·(3+2i) (2+i)$^2$·(3−2i) i·(2−i)$^2$·(3−2i) |
| 328 | 2+18i 18+2i | −i·(1+i)$^3$·(5+4i) −i·(1+i)$^3$·(5−4i) |
| 333 | 3+18i 18+3i | i·3·(6−i) 3·(6+i) |
| 337 | 9+16i 16+9i | (p) (p) |
| 338 | 7+17i 13+13i 17+7i | i·(1+i)·(3−2i)$^2$ (1+i)·(3+2i)·(3−2i) −i·(1+i)·(3+2i)$^2$ |
| 340 | 4+18i 12+14i 14+12i 18+4i | (1+i)$^2$·(2−i)·(4+i) (1+i)$^2$·(2−i)·(4−i) −i·(1+i)$^2$·(2+i)·(4+i) −i·(1+i)$^2$·(2+i)·(4−i) |
| 346 | 11+15i 15+11i | (1+i)·(13+2i) (1+i)·(13−2i) |
| 349 | 5+18i 18+5i | (p) (p) |
| 353 | 8+17i 17+8i | (p) (p) |
| 356 | 10+16i 16+10i | (1+i)$^2$·(8−5i) −i·(1+i)$^2$·(8+5i) |
| 360 | 6+18i 18+6i | −i·(1+i)$^3$·(2+i)·3 −i·(1+i)$^3$·(2−i)·3 |
| 361 | 19 | (p) |
| 362 | 1+19i 19+i | (1+i)·(10+9i) (1+i)·(10−9i) |
| 365 | 2+19i 13+14i 14+13i 19+2i | i·(2−i)·(8+3i) (2+i)·(8+3i) i·(2−i)·(8−3i) (2+i)·(8−3i) |
| 369 | 12+15i 15+12i | i·3·(5−4i) 3·(5+4i) |
| 370 | 3+19i 9+17i 17+9i 19+3i | (1+i)·(2+i)·(6+i) (1+i)·(2+i)·(6−i) (1+i)·(2−i)·(6+i) (1+i)·(2−i)·(6−i) |
| 373 | 7+18i 18+7i | (p) (p) |
| 377 | 4+19i 11+16i 16+11i 19+4i | i·(3−2i)·(5+2i) (3+2i)·(5+2i) i·(3−2i)·(5−2i) (3+2i)·(5−2i) |
| 386 | 5+19i 19+5i | (1+i)·(12+7i) (1+i)·(12−7i) |
| 388 | 8+18i 18+8i | (1+i)$^2$·(9−4i) −i·(1+i)$^2$·(9+4i) |
| 389 | 10+17i 17+10i | (p) (p) |
| 392 | 14+14i | −i·(1+i)$^3$·7 |
| 394 | 13+15i 15+13i | (1+i)·(14+i) (1+i)·(14−i) |
| 397 | 6+19i 19+6i | (p) (p) |
| 400 | 12+16i 16+12i 20 | −(1+i)$^4$·(2+i)$^2$ −i·(1+i)$^4$·(2−i)$^2$ −(1+i)$^4$·(2+i)·(2−i) |
| 401 | 1+20i 20+i | (p) (p) |
| 404 | 2+20i 20+2i | (1+i)$^2$·(10−i) −i·(1+i)$^2$·(10+i) |
| 405 | 9+18i 18+9i | i·(2−i)·3$^2$ (2+i)·3$^2$ |
| 409 | 3+20i 20+3i | (p) (p) |
| 410 | 7+19i 11+17i 17+11i 19+7i | i·(1+i)·(2−i)·(5−4i) (1+i)·(2−i)·(5+4i) (1+i)·(2+i)·(5−4i) −i·(1+i)·(2+i)·(5+4i) |
| 416 | 4+20i 20+4i | −(1+i)$^5$·(3+2i) −(1+i)$^5$·(3−2i) |
| 421 | 14+15i 15+14i | (p) (p) |
| 424 | 10+18i 18+10i | −i·(1+i)$^3$·(7+2i) −i·(1+i)$^3$·(7−2i) |
| 425 | 5+20i 8+19i 13+16i 16+13i 19+8i 20+5i | i·(2+i)·(2−i)·(4−i) (2+i)$^2$·(4+i) i·(2−i)$^2$·(4+i) (2+i)$^2$·(4−i) i·(2−i)$^2$·(4−i) (2+i)·(2−i)·(4+i) |
| 433 | 12+17i 17+12i | (p) (p) |
| 436 | 6+20i 20+6i | (1+i)$^2$·(10−3i) −i·(1+i)$^2$·(10+3i) |
| 441 | 21 | 3·7 |
| 442 | 1+21i 9+19i 19+9i 21+i | i·(1+i)·(3−2i)·(4−i) (1+i)·(3+2i)·(4−i) (1+i)·(3−2i)·(4+i) −i·(1+i)·(3+2i)·(4+i) |
| 445 | 2+21i 11+18i 18+11i 21+2i | i·(2+i)·(8−5i) (2+i)·(8+5i) i·(2−i)·(8−5i) (2−i)·(8+5i) |
| 449 | 7+20i 20+7i | (p) (p) |
| 450 | 3+21i 15+15i 21+3i | i·(1+i)·(2−i)$^2$·3 (1+i)·(2+i)·(2−i)·3 −i·(1+i)·(2+i)$^2$·3 |
| 452 | 14+16i 16+14i | (1+i)$^2$·(8−7i) −i·(1+i)$^2$·(8+7i) |
| 457 | 4+21i 21+4i | (p) (p) |
| 458 | 13+17i 17+13i | (1+i)·(15+2i) (1+i)·(15−2i) |
| 461 | 10+19i 19+10i | (p) (p) |
| 464 | 8+20i 20+8i | −i·(1+i)$^4$·(5−2i) −(1+i)$^4$·(5+2i) |
| 466 | 5+21i 21+5i | (1+i)·(13+8i) (1+i)·(13−8i) |
| 468 | 12+18i 18+12i | (1+i)$^2$·3·(3−2i) −i·(1+i)$^2$·3·(3+2i) |
| 477 | 6+21i 21+6i | i·3·(7−2i) 3·(7+2i) |
| 481 | 9+20i 15+16i 16+15i 20+9i | i·(3−2i)·(6+i) i·(3−2i)·(6−i) (3+2i)·(6+i) (3+2i)·(6−i) |
| 482 | 11+19i 19+11i | (1+i)·(15+4i) (1+i)·(15−4i) |
| 484 | 22 | −i·(1+i)$^2$·11 |
| 485 | 1+22i 14+17i 17+14i 22+i | i·(2−i)·(9+4i) (2+i)·(9+4i) i·(2−i)·(9−4i) (2+i)·(9−4i) |
| 488 | 2+22i 22+2i | −i·(1+i)$^3$·(6+5i) −i·(1+i)$^3$·(6−5i) |
| 490 | 7+21i 21+7i | (1+i)·(2+i)·7 (1+i)·(2−i)·7 |
| 493 | 3+22i 13+18i 18+13i 22+3i | i·(4+i)·(5−2i) i·(4−i)·(5−2i) (4+i)·(5+2i) (4−i)·(5+2i) |
| 500 | 4+22i 10+20i 20+10i 22+4i | −i·(1+i)$^2$·(2+i)$^3$ (1+i)$^2$·(2+i)·(2−i)$^2$ −i·(1+i)$^2$·(2+i)$^2$·(2−i) (1+i)$^2$·(2−i)$^3$ |
| المعيار | العدد الصحيح | العوامل |
| 505 | 8+21i 12+19i 19+12i 21+8i | i·(2−i)·(10+i) i·(2−i)·(10−i) (2+i)·(10+i) (2+i)·(10−i) |
| 509 | 5+22i 22+5i | (p) (p) |
| 512 | 16+16i | (1+i)$^9$ |
| 514 | 15+17i 17+15i | (1+i)·(16+i) (1+i)·(16−i) |
| 520 | 6+22i 14+18i 18+14i 22+6i | (1+i)$^3$·(2−i)·(3−2i) −i·(1+i)$^3$·(2−i)·(3+2i) −i·(1+i)$^3$·(2+i)·(3−2i) −(1+i)$^3$·(2+i)·(3+2i) |
| 521 | 11+20i 20+11i | (p) (p) |
| 522 | 9+21i 21+9i | (1+i)·3·(5+2i) (1+i)·3·(5−2i) |
| 529 | 23 | (p) |
| 530 | 1+23i 13+19i 19+13i 23+i | (1+i)·(2+i)·(7+2i) (1+i)·(2+i)·(7−2i) (1+i)·(2−i)·(7+2i) (1+i)·(2−i)·(7−2i) |
| 533 | 2+23i 7+22i 22+7i 23+2i | i·(3+2i)·(5−4i) (3+2i)·(5+4i) i·(3−2i)·(5−4i) (3−2i)·(5+4i) |
| 538 | 3+23i 23+3i | (1+i)·(13+10i) (1+i)·(13−10i) |
| 541 | 10+21i 21+10i | (p) (p) |
| 544 | 12+20i 20+12i | −(1+i)$^5$·(4+i) −(1+i)$^5$·(4−i) |
| 545 | 4+23i 16+17i 17+16i 23+4i | i·(2−i)·(10+3i) i·(2−i)·(10−3i) (2+i)·(10+3i) (2+i)·(10−3i) |
| 548 | 8+22i 22+8i | (1+i)$^2$·(11−4i) −i·(1+i)$^2$·(11+4i) |
| 549 | 15+18i 18+15i | i·3·(6−5i) 3·(6+5i) |
| 554 | 5+23i 23+5i | (1+i)·(14+9i) (1+i)·(14−9i) |
| 557 | 14+19i 19+14i | (p) (p) |
| 562 | 11+21i 21+11i | (1+i)·(16+5i) (1+i)·(16−5i) |
| 565 | 6+23i 9+22i 22+9i 23+6i | i·(2+i)·(8−7i) (2+i)·(8+7i) i·(2−i)·(8−7i) (2−i)·(8+7i) |
| 569 | 13+20i 20+13i | (p) (p) |
| 576 | 24 | i·(1+i)$^6$·3 |
| 577 | 1+24i 24+i | (p) (p) |
| 578 | 7+23i 17+17i 23+7i | (1+i)·(4+i)$^2$ (1+i)·(4+i)·(4−i) (1+i)·(4−i)$^2$ |
| 580 | 2+24i 16+18i 18+16i 24+2i | (1+i)$^2$·(2−i)·(5+2i) −i·(1+i)$^2$·(2+i)·(5+2i) (1+i)$^2$·(2−i)·(5−2i) −i·(1+i)$^2$·(2+i)·(5−2i) |
| 584 | 10+22i 22+10i | −i·(1+i)$^3$·(8+3i) −i·(1+i)$^3$·(8−3i) |
| 585 | 3+24i 12+21i 21+12i 24+3i | i·(2+i)·3·(3−2i) (2+i)·3·(3+2i) i·(2−i)·3·(3−2i) (2−i)·3·(3+2i) |
| 586 | 15+19i 19+15i | (1+i)·(17+2i) (1+i)·(17−2i) |
| 592 | 4+24i 24+4i | −i·(1+i)$^4$·(6−i) −(1+i)$^4$·(6+i) |
| 593 | 8+23i 23+8i | (p) (p) |
| 596 | 14+20i 20+14i | (1+i)$^2$·(10−7i) −i·(1+i)$^2$·(10+7i) |
| 601 | 5+24i 24+5i | (p) (p) |
| 605 | 11+22i 22+11i | i·(2−i)·11 (2+i)·11 |
| 610 | 9+23i 13+21i 21+13i 23+9i | i·(1+i)·(2−i)·(6−5i) (1+i)·(2−i)·(6+5i) (1+i)·(2+i)·(6−5i) −i·(1+i)·(2+i)·(6+5i) |
| 612 | 6+24i 24+6i | (1+i)$^2$·3·(4−i) −i·(1+i)$^2$·3·(4+i) |
| 613 | 17+18i 18+17i | (p) (p) |
| 617 | 16+19i 19+16i | (p) (p) |
| 625 | 7+24i 15+20i 20+15i 24+7i 25 | −(2−i)$^4$ (2+i)$^3$·(2−i) i·(2+i)·(2−i)$^3$ −i·(2+i)$^4$ (2+i)$^2$·(2−i)$^2$ |
| 626 | 1+25i 25+i | (1+i)·(13+12i) (1+i)·(13−12i) |
| 628 | 12+22i 22+12i | (1+i)$^2$·(11−6i) −i·(1+i)$^2$·(11+6i) |
| 629 | 2+25i 10+23i 23+10i 25+2i | i·(4−i)·(6+i) i·(4−i)·(6−i) (4+i)·(6+i) (4+i)·(6−i) |
| 634 | 3+25i 25+3i | (1+i)·(14+11i) (1+i)·(14−11i) |
| 637 | 14+21i 21+14i | i·(3−2i)·7 (3+2i)·7 |
| 640 | 8+24i 24+8i | i·(1+i)$^7$·(2+i) i·(1+i)$^7$·(2−i) |
| 641 | 4+25i 25+4i | (p) (p) |
| 648 | 18+18i | −i·(1+i)$^3$·3$^2$ |
| 650 | 5+25i 11+23i 17+19i 19+17i 23+11i 25+5i | (1+i)·(2+i)·(2−i)·(3+2i) (1+i)·(2+i)$^2$·(3−2i) i·(1+i)·(2−i)$^2$·(3−2i) −i·(1+i)·(2+i)$^2$·(3+2i) (1+i)·(2−i)$^2$·(3+2i) (1+i)·(2+i)·(2−i)·(3−2i) |
| 653 | 13+22i 22+13i | (p) (p) |
| 656 | 16+20i 20+16i | −i·(1+i)$^4$·(5−4i) −(1+i)$^4$·(5+4i) |
| 657 | 9+24i 24+9i | i·3·(8−3i) 3·(8+3i) |
| 661 | 6+25i 25+6i | (p) (p) |
| 666 | 15+21i 21+15i | (1+i)·3·(6+i) (1+i)·3·(6−i) |
| 673 | 12+23i 23+12i | (p) (p) |
| 674 | 7+25i 25+7i | (1+i)·(16+9i) (1+i)·(16−9i) |
| 676 | 10+24i 24+10i 26 | −i·(1+i)$^2$·(3+2i)$^2$ (1+i)$^2$·(3−2i)$^2$ −i·(1+i)$^2$·(3+2i)·(3−2i) |
| 677 | 1+26i 26+i | (p) (p) |
| 680 | 2+26i 14+22i 22+14i 26+2i | −i·(1+i)$^3$·(2+i)·(4+i) −i·(1+i)$^3$·(2+i)·(4−i) −i·(1+i)$^3$·(2−i)·(4+i) −i·(1+i)$^3$·(2−i)·(4−i) |
| 685 | 3+26i 18+19i 19+18i 26+3i | i·(2−i)·(11+4i) (2+i)·(11+4i) i·(2−i)·(11−4i) (2+i)·(11−4i) |
| 689 | 8+25i 17+20i 20+17i 25+8i | i·(3−2i)·(7+2i) (3+2i)·(7+2i) i·(3−2i)·(7−2i) (3+2i)·(7−2i) |
| 692 | 4+26i 26+4i | (1+i)$^2$·(13−2i) −i·(1+i)$^2$·(13+2i) |
| 697 | 11+24i 16+21i 21+16i 24+11i | i·(4+i)·(5−4i) (4+i)·(5+4i) i·(4−i)·(5−4i) (4−i)·(5+4i) |
| 698 | 13+23i 23+13i | (1+i)·(18+5i) (1+i)·(18−5i) |
| 701 | 5+26i 26+5i | (p) (p) |
| 706 | 9+25i 25+9i | (1+i)·(17+8i) (1+i)·(17−8i) |
| 709 | 15+22i 22+15i | (p) (p) |
| 712 | 6+26i 26+6i | −i·(1+i)$^3$·(8+5i) −i·(1+i)$^3$·(8−5i) |
| 720 | 12+24i 24+12i | −i·(1+i)$^4$·(2−i)·3 −(1+i)$^4$·(2+i)·3 |
| 722 | 19+19i | (1+i)·19 |
| 724 | 18+20i 20+18i | (1+i)$^2$·(10−9i) −i·(1+i)$^2$·(10+9i) |
| 725 | 7+26i 10+25i 14+23i 23+14i 25+10i 26+7i | (2+i)$^2$·(5+2i) i·(2+i)·(2−i)·(5−2i) i·(2−i)$^2$·(5+2i) (2+i)$^2$·(5−2i) (2+i)·(2−i)·(5+2i) i·(2−i)$^2$·(5−2i) |
| 729 | 27 | 3$^3$ |
| 730 | 1+27i 17+21i 21+17i 27+i | i·(1+i)·(2−i)·(8−3i) (1+i)·(2+i)·(8−3i) (1+i)·(2−i)·(8+3i) −i·(1+i)·(2+i)·(8+3i) |
| 733 | 2+27i 27+2i | (p) (p) |
| 738 | 3+27i 27+3i | (1+i)·3·(5+4i) (1+i)·3·(5−4i) |
| 740 | 8+26i 16+22i 22+16i 26+8i | (1+i)$^2$·(2−i)·(6+i) (1+i)$^2$·(2−i)·(6−i) −i·(1+i)$^2$·(2+i)·(6+i) −i·(1+i)$^2$·(2+i)·(6−i) |
| 745 | 4+27i 13+24i 24+13i 27+4i | i·(2+i)·(10−7i) (2+i)·(10+7i) i·(2−i)·(10−7i) (2−i)·(10+7i) |
| 746 | 11+25i 25+11i | (1+i)·(18+7i) (1+i)·(18−7i) |
| المعيار | العدد الصحيح | العوامل |
| 754 | 5+27i 15+23i 23+15i 27+5i | i·(1+i)·(3−2i)·(5−2i) (1+i)·(3+2i)·(5−2i) (1+i)·(3−2i)·(5+2i) −i·(1+i)·(3+2i)·(5+2i) |
| 757 | 9+26i 26+9i | (p) (p) |
| 761 | 19+20i 20+19i | (p) (p) |
| 765 | 6+27i 18+21i 21+18i 27+6i | i·(2−i)·3·(4+i) i·(2−i)·3·(4−i) (2+i)·3·(4+i) (2+i)·3·(4−i) |
| 769 | 12+25i 25+12i | (p) (p) |
| 772 | 14+24i 24+14i | (1+i)$^2$·(12−7i) −i·(1+i)$^2$·(12+7i) |
| 773 | 17+22i 22+17i | (p) (p) |
| 776 | 10+26i 26+10i | −i·(1+i)$^3$·(9+4i) −i·(1+i)$^3$·(9−4i) |
| 778 | 7+27i 27+7i | (1+i)·(17+10i) (1+i)·(17−10i) |
| 784 | 28 | −(1+i)$^4$·7 |
| 785 | 1+28i 16+23i 23+16i 28+i | i·(2+i)·(11−6i) (2+i)·(11+6i) i·(2−i)·(11−6i) (2−i)·(11+6i) |
| 788 | 2+28i 28+2i | (1+i)$^2$·(14−i) −i·(1+i)$^2$·(14+i) |
| 793 | 3+28i 8+27i 27+8i 28+3i | i·(3+2i)·(6−5i) (3+2i)·(6+5i) i·(3−2i)·(6−5i) (3−2i)·(6+5i) |
| 794 | 13+25i 25+13i | (1+i)·(19+6i) (1+i)·(19−6i) |
| 797 | 11+26i 26+11i | (p) (p) |
| 800 | 4+28i 20+20i 28+4i | −i·(1+i)$^5$·(2−i)$^2$ −(1+i)$^5$·(2+i)·(2−i) i·(1+i)$^5$·(2+i)$^2$ |
| 801 | 15+24i 24+15i | i·3·(8−5i) 3·(8+5i) |
| 802 | 19+21i 21+19i | (1+i)·(20+i) (1+i)·(20−i) |
| 808 | 18+22i 22+18i | −i·(1+i)$^3$·(10+i) −i·(1+i)$^3$·(10−i) |
| 809 | 5+28i 28+5i | (p) (p) |
| 810 | 9+27i 27+9i | (1+i)·(2+i)·3$^2$ (1+i)·(2−i)·3$^2$ |
| 818 | 17+23i 23+17i | (1+i)·(20+3i) (1+i)·(20−3i) |
| 820 | 6+28i 12+26i 26+12i 28+6i | (1+i)$^2$·(2+i)·(5−4i) −i·(1+i)$^2$·(2+i)·(5+4i) (1+i)$^2$·(2−i)·(5−4i) −i·(1+i)$^2$·(2−i)·(5+4i) |
| 821 | 14+25i 25+14i | (p) (p) |
| 829 | 10+27i 27+10i | (p) (p) |
| 832 | 16+24i 24+16i | −(1+i)$^6$·(3−2i) i·(1+i)$^6$·(3+2i) |
| 833 | 7+28i 28+7i | i·(4−i)·7 (4+i)·7 |
| 841 | 20+21i 21+20i 29 | i·(5−2i)$^2$ (5+2i)$^2$ (5+2i)·(5−2i) |
| 842 | 1+29i 29+i | (1+i)·(15+14i) (1+i)·(15−14i) |
| 845 | 2+29i 13+26i 19+22i 22+19i 26+13i 29+2i | −(2−i)·(3−2i)$^2$ i·(2−i)·(3+2i)·(3−2i) i·(2+i)·(3−2i)$^2$ (2−i)·(3+2i)$^2$ (2+i)·(3+2i)·(3−2i) −i·(2+i)·(3+2i)$^2$ |
| 848 | 8+28i 28+8i | −i·(1+i)$^4$·(7−2i) −(1+i)$^4$·(7+2i) |
| 850 | 3+29i 11+27i 15+25i 25+15i 27+11i 29+3i | (1+i)·(2+i)$^2$·(4−i) i·(1+i)·(2−i)$^2$·(4−i) (1+i)·(2+i)·(2−i)·(4+i) (1+i)·(2+i)·(2−i)·(4−i) −i·(1+i)·(2+i)$^2$·(4+i) (1+i)·(2−i)$^2$·(4+i) |
| 853 | 18+23i 23+18i | (p) (p) |
| 857 | 4+29i 29+4i | (p) (p) |
| 865 | 9+28i 17+24i 24+17i 28+9i | i·(2−i)·(13+2i) i·(2−i)·(13−2i) (2+i)·(13+2i) (2+i)·(13−2i) |
| 866 | 5+29i 29+5i | (1+i)·(17+12i) (1+i)·(17−12i) |
| 872 | 14+26i 26+14i | −i·(1+i)$^3$·(10+3i) −i·(1+i)$^3$·(10−3i) |
| 873 | 12+27i 27+12i | i·3·(9−4i) 3·(9+4i) |
| 877 | 6+29i 29+6i | (p) (p) |
| 881 | 16+25i 25+16i | (p) (p) |
| 882 | 21+21i | (1+i)·3·7 |
| 884 | 10+28i 20+22i 22+20i 28+10i | (1+i)$^2$·(3−2i)·(4+i) −i·(1+i)$^2$·(3+2i)·(4+i) (1+i)$^2$·(3−2i)·(4−i) −i·(1+i)$^2$·(3+2i)·(4−i) |
| 890 | 7+29i 19+23i 23+19i 29+7i | i·(1+i)·(2−i)·(8−5i) (1+i)·(2−i)·(8+5i) (1+i)·(2+i)·(8−5i) −i·(1+i)·(2+i)·(8+5i) |
| 898 | 13+27i 27+13i | (1+i)·(20+7i) (1+i)·(20−7i) |
| 900 | 18+24i 24+18i 30 | −i·(1+i)$^2$·(2+i)$^2$·3 (1+i)$^2$·(2−i)$^2$·3 −i·(1+i)$^2$·(2+i)·(2−i)·3 |
| 901 | 1+30i 15+26i 26+15i 30+i | i·(4+i)·(7−2i) i·(4−i)·(7−2i) (4+i)·(7+2i) (4−i)·(7+2i) |
| 904 | 2+30i 30+2i | −i·(1+i)$^3$·(8+7i) −i·(1+i)$^3$·(8−7i) |
| 905 | 8+29i 11+28i 28+11i 29+8i | i·(2+i)·(10−9i) (2+i)·(10+9i) i·(2−i)·(10−9i) (2−i)·(10+9i) |
| 909 | 3+30i 30+3i | i·3·(10−i) 3·(10+i) |
| 914 | 17+25i 25+17i | (1+i)·(21+4i) (1+i)·(21−4i) |
| 916 | 4+30i 30+4i | (1+i)$^2$·(15−2i) −i·(1+i)$^2$·(15+2i) |
| 922 | 9+29i 29+9i | (1+i)·(19+10i) (1+i)·(19−10i) |
| 925 | 5+30i 14+27i 21+22i 22+21i 27+14i 30+5i | i·(2+i)·(2−i)·(6−i) (2+i)$^2$·(6+i) i·(2−i)$^2$·(6+i) (2+i)$^2$·(6−i) i·(2−i)$^2$·(6−i) (2+i)·(2−i)·(6+i) |
| 928 | 12+28i 28+12i | −(1+i)$^5$·(5+2i) −(1+i)$^5$·(5−2i) |
| 929 | 20+23i 23+20i | (p) (p) |
| 932 | 16+26i 26+16i | (1+i)$^2$·(13−8i) −i·(1+i)$^2$·(13+8i) |
| 936 | 6+30i 30+6i | −i·(1+i)$^3$·3·(3+2i) −i·(1+i)$^3$·3·(3−2i) |
| 937 | 19+24i 24+19i | (p) (p) |
| 941 | 10+29i 29+10i | (p) (p) |
| 949 | 7+30i 18+25i 25+18i 30+7i | i·(3−2i)·(8+3i) (3+2i)·(8+3i) i·(3−2i)·(8−3i) (3+2i)·(8−3i) |
| 953 | 13+28i 28+13i | (p) (p) |
| 954 | 15+27i 27+15i | (1+i)·3·(7+2i) (1+i)·3·(7−2i) |
| 961 | 31 | (p) |
| 962 | 1+31i 11+29i 29+11i 31+i | (1+i)·(3+2i)·(6+i) (1+i)·(3+2i)·(6−i) (1+i)·(3−2i)·(6+i) (1+i)·(3−2i)·(6−i) |
| 964 | 8+30i 30+8i | (1+i)$^2$·(15−4i) −i·(1+i)$^2$·(15+4i) |
| 965 | 2+31i 17+26i 26+17i 31+2i | i·(2+i)·(12−7i) (2+i)·(12+7i) i·(2−i)·(12−7i) (2−i)·(12+7i) |
| 968 | 22+22i | −i·(1+i)$^3$·11 |
| 970 | 3+31i 21+23i 23+21i 31+3i | i·(1+i)·(2−i)·(9−4i) (1+i)·(2+i)·(9−4i) (1+i)·(2−i)·(9+4i) −i·(1+i)·(2+i)·(9+4i) |
| 976 | 20+24i 24+20i | −i·(1+i)$^4$·(6−5i) −(1+i)$^4$·(6+5i) |
| 977 | 4+31i 31+4i | (p) (p) |
| 980 | 14+28i 28+14i | (1+i)$^2$·(2−i)·7 −i·(1+i)$^2$·(2+i)·7 |
| 981 | 9+30i 30+9i | i·3·(10−3i) 3·(10+3i) |
| 985 | 12+29i 16+27i 27+16i 29+12i | i·(2−i)·(14+i) i·(2−i)·(14−i) (2+i)·(14+i) (2+i)·(14−i) |
| 986 | 5+31i 19+25i 25+19i 31+5i | (1+i)·(4+i)·(5+2i) (1+i)·(4−i)·(5+2i) (1+i)·(4+i)·(5−2i) (1+i)·(4−i)·(5−2i) |
| 997 | 6+31i 31+6i | (p) (p) |
| 1000 | 10+30i 18+26i 26+18i 30+10i | −i·(1+i)$^3$·(2+i)$^2$·(2−i) (1+i)$^3$·(2−i)$^3$ −(1+i)$^3$·(2+i)$^3$ −i·(1+i)$^3$·(2+i)·(2−i)$^2$ |

## مراجع

* ↑ "معلومات عن جدول تفكيك الأعداد الصحيحة الغاوسية على موقع mathworld.wolfram.com". mathworld.wolfram.com. مؤرشف من الأصل في 2018-12-17.

## وصلات خارجية

* إيريك ويستاين، Gaussian prime، ماثوورلد Mathworld (باللغة الإنكليزية).
* إيريك ويستاين، Prime Factorization، ماثوورلد Mathworld (باللغة الإنكليزية).
* OEIS: Gaussian Primes

## طالع أيضا

* جدول التفكيك إلى عوامل أولية
* جدول القواعد
* بوابة رياضيات
* هذه بذرة مقالة عن الرياضيات او موضوع متعلق بها بحاجة للتوسيع. فضلًا شارك في تحريرها.